How to change subdivisions after adding a grid
Immediately after adding the grid (See here for details as to why it has to be immediate) you can access various options at the bottom of the 3D toolbar (where it says Toggle Editmode in your screenshot) such as the x and y subdivisions:



You can also access these options (again, immediately after adding the grid) by pressing F6.

So you should:


Add the grid.
Increase x and y subdivisions as desired.
Then scale the grid up as much as you want.